Algebra Examples

$\sqrt{8 y} + 5 \sqrt{50 y} - 2 \sqrt{18 y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8 y$ as $2^{2} \cdot (2 y)$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) y} + 5 \sqrt{50 y} - 2 \sqrt{18 y}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 2 y} + 5 \sqrt{50 y} - 2 \sqrt{18 y}$

Step 1.1.3

Add parentheses.

$\sqrt{2^{2} \cdot (2 y)} + 5 \sqrt{50 y} - 2 \sqrt{18 y}$

Step 1.2

Pull terms out from under the radical.

$| 2 | \sqrt{2 y} + 5 \sqrt{50 y} - 2 \sqrt{18 y}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$2 \sqrt{2 y} + 5 \sqrt{50 y} - 2 \sqrt{18 y}$

Step 1.4

Rewrite $50 y$ as $5^{2} \cdot (2 y)$ .

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Step 1.4.1

Factor $25$ out of $50$ .

$2 \sqrt{2 y} + 5 \sqrt{25 (2) y} - 2 \sqrt{18 y}$

Step 1.4.2

Rewrite $25$ as $5^{2}$ .

$2 \sqrt{2 y} + 5 \sqrt{5^{2} \cdot 2 y} - 2 \sqrt{18 y}$

Step 1.4.3

Add parentheses.

$2 \sqrt{2 y} + 5 \sqrt{5^{2} \cdot (2 y)} - 2 \sqrt{18 y}$

Step 1.5

Pull terms out from under the radical.

$2 \sqrt{2 y} + 5 (| 5 | \sqrt{2 y}) - 2 \sqrt{18 y}$

Step 1.6

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$2 \sqrt{2 y} + 5 (5 \sqrt{2 y}) - 2 \sqrt{18 y}$

Step 1.7

Multiply $5$ by $5$ .

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 2 \sqrt{18 y}$

Step 1.8

Rewrite $18 y$ as $3^{2} \cdot (2 y)$ .

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Step 1.8.1

Factor $9$ out of $18$ .

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 2 \sqrt{9 (2) y}$

Step 1.8.2

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 2 \sqrt{3^{2} \cdot 2 y}$

Step 1.8.3

Add parentheses.

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 2 \sqrt{3^{2} \cdot (2 y)}$

Step 1.9

Pull terms out from under the radical.

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 2 (| 3 | \sqrt{2 y})$

Step 1.10

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 2 (3 \sqrt{2 y})$

Step 1.11

Multiply $3$ by $- 2$ .

$2 \sqrt{2 y} + 25 \sqrt{2 y} - 6 \sqrt{2 y}$

Step 2

Add $2 \sqrt{2 y}$ and $25 \sqrt{2 y}$ .

$27 \sqrt{2 y} - 6 \sqrt{2 y}$

Step 3

Subtract $6 \sqrt{2 y}$ from $27 \sqrt{2 y}$ .

$21 \sqrt{2 y}$